Optimal inflation target: Insights from an agentbased model

Bouchaud, Jean-Philippe; Gualdi, Stanislao; Tarzia, Marco; Zamponi, Francesco Working Paper Optimal inflation target: Insights from an agentbased model Economics Discussion Papers, No. 2017-64 Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Bouchaud, Jean-Philippe; Gualdi, Stanislao; Tarzia, Marco; Zamponi, Francesco (2017) : Optimal inflation target: Insights from an agentbased model, Economics Discussion Papers, No. 2017-64, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: https://hdl.handle.net/10419/169123 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Licensed under the Creative Commons License - Attribution 4.0 International (CC BY 4.0) Discussion Paper No. 2017-64 | September 25, 2017 | http://www.economics-ejournal.org/economics/discussionpapers/2017-64 Optimal inflation target: insights from an agentbased model Jean-Philippe Bouchaud, Stanislao Gualdi, Marco Tarzia, and Francesco Zamponi Abstract Which level of inflation should Central Banks be targeting? The authors investigate this issue in the context of a simplified Agent Based Model of the economy. Depending on the value of the parameters that describe the micro-behaviour of agents (in particular inflation anticipations), they find a surprisingly rich variety of behaviour at the macrolevel. Without any monetary policy, our ABM economy can be in a high inflation/high output state, or in a low inflation/low output state. Hyper-inflation, stagflation, deflation and business cycles are also possible. The authors then introduce a Central Bank with a Taylor-rule-based inflation target, and study the resulting aggregate variables. The main result is that too low inflation targets are in general detrimental to a CB-controlled economy. One symptom is a persistent under-realisation of inflation, perhaps similar to the current macroeconomic situation. This predicament is alleviated by higher inflation targets that are found to improve both unemployment and negative interest rate episodes, up to the point where erosion of savings becomes unacceptable. The results are contrasted with the predictions of the standard DSGE model. (Published in Special Issue Agent-based modelling and complexity economics) JEL E31 E32 E52 Keywords Agent based models; monetary policy; inflation target; Taylor rule Authors Jean-Philippe Bouchaud, CFM, 23 rue de l’Université, 75007 Paris, France, Jean- [email protected] Stanislao Gualdi, CFM, 23 rue de l’Université, 75007 Paris, France Marco Tarzia, Université Pierre et Marie Curie – Paris 6, Laboratoire de Physique Théorique de la Matière Condensée, 4, Place Jussieu, Tour 12, 75252 Paris Cedex 05, France Francesco Zamponi, Laboratoire de physique théorique, Département de physique de l’ENS, École normale supérieure, PSL Research University, Sorbonne Universités, UPMC Univ. Paris 06, CNRS, 75005 Paris, France Citation Jean-Philippe Bouchaud, Stanislao Gualdi, Marco Tarzia, and Francesco Zamponi (2017). Optimal inflation target: insights from an agent-based model. Economics Discussion Papers, No 2017-64, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2017-64 2 I. INTRODUCTION Most Central Banks around the world nowadays adjust their monetary policy to reach a 2%/year inflation target. The rationale for choosing 2% rather than 1% or 3% is however not clear, as with many other “magic numbers” religiously used in economic policy. The recent crisis has put to the fore the problem of negative nominal interest rates, which can be seen as a consequence of low inflation targets and thus low baseline rates. As emphasized by O. Blanchard in 2010 [1], “As a matter of logic, higher average inflation and thus higher average nominal interest rates before the crisis would have given more room for monetary policy to be eased during the crisis.” This view is however disputed by many economists, who strongly argue against a raise of the inflation target (see e.g. [2, 3] for a recent overview). A major argument to that effect is the credibility of Central Banks, who have succeeded in anchoring low-inflation expectations in the minds of economic agents. If the inflation target is changed in the face of new circumstances, these expectations may un-moor, and the very efficiency of monetary policy may suffer as a consequence. Clearly, the fear of a lurking run-away inflation is weighing heavily on the debate. Yet, the question of an “optimal” inflation target is well worth considering, and policy makers are eager to receive inputs from academic research. As Federal Reserve Chairwoman J. Yellen recently declared [4]: “We very much look forward to seeing research by economists that will help inform our future decisions on this”. Of course, optimality needs to be defined and different criteria (i.e. welfare functions) may lead to different results. More important still is the modelling framework used to describe the economy. A clear puzzle is that standard monetary theories imply zero or negative optimal inflation rates, at variance with Central Banks’ inflation targets [5]. The standard DSGE machinery – the “workhorse” of monetary economists [6] – has recently been extended to cope with non-zero inflation rates, and generally concludes that the optimal inflation rate should be smaller than 2% [7]. However, DSGE models are based on a series of highly debatable assumptions, and have been under intense fire after the 2007 crisis [8–11]. Another route is provided by Agent Based Models (ABM) in which “reasonable” behavioural rules replace the representative DSGE agent with a fully rational long-term plan. ABMs can include a number of economically relevant features which would be very difficult to accommodate within the DSGE straight-jacket [12–15]. Many simplifying assumptions are of course necessary, but a considerable advantage of ABMs is that interaction-induced, collective effects are present, when DSGE models reduce the whole economy to a small number of representative agents. As a consequence, the global “equilibrium” state of the economy is an emergent property in the former case, while it is a deus ex machina in the latter case. In particular, crises (i.e. large swings in the output) can occur endogenously within ABMs [16, 17]. DSGE models, on the other hand, only describe small, mean-reverting fluctuations around the postulated equilibrium and crises can only result from exogenous, unpredictable shocks.1As a case in point, we found in [19] that the aggregate behavior of the economy is not a smooth function of the baseline interest rate: the fact that firms are risk averse and fear going into debt leads to more unemployment that can spiral into a destabilizing feedback loop. This is one of Blanchard’s “dark corners” [20] that ABMs can help uncovering. To our knowledge, the optimal inflation target question has not been investigated using ABMs (although see [21] where the efficiency of inflation targeting policies is discussed within the framework of an ABM). In the present paper, we take on this issue using a simplified, bare-bone ABM dubbed “Mark-0”, studied in great details in [17, 19], following previous work by the group of Delli Gatti et al. [16] (see also [21, 22]). As discussed in [17], the Mark-0 economy can be in different states or “phases”, good or bad, depending on various parameters. These parameters describe in a phenomenological way the behaviour of agents (firms, households and banks), and their response to different economic stimuli. Interestingly, small changes in the value of these parameters can indeed induce sharp variations in aggregate output, unemployment or inflation [17, 19]. This allows us to consider different “baseline” economies (high inflation/low unemployment, or low inflation/high unemployment) and study the influence of the chosen inflation target on the total output, on the real interest rate and on the probability of negative nominal interest rates. Our main conclusion is that in general, increasing the inflation target reduces unemployment and reduces the probability of negative rates. Unsurprisingly, it also reduces real interest rates on savings. Actually, trying to impose low inflation on an economy that would naturally run at full steam with high inflation can lead to a complete collapse (high unemployment and deflation). However, high inflation policies can be dangerous and may generate hyper-inflation if agents lose faith in the ability of Central Banks to fulfill their mandate. Our results are based on a stylized model that is arguably unrealistic on several counts – but the very same can be said about DSGE models. Still, the Mark-0 model, although highly simplified, contains plausible ingredients that are most probably present in reality. For example, our model encodes in a schematic manner the consumption 1R. Lucas famously argued that the 2008 crisis was not predicted because economic theory predicts that such events cannot be predicted [18]. 3 behavior of households facing inflation, that is in fact similar to the standard Euler equation for consumption in general equilibrium models [6]. On the other hand, the effect of inflation on the behaviour of indebted firms appears to be absent in DSGE models. The fact that our results strongly contrast with those of standard DSGE models is in our opinion enough to warrant in-depth investigations of more realistic ABMs, and more empirical work on the micro/behavioural assumptions that underpin these models. Disclaimer: the parameters chosen in the following are not the result of a precise calibration. We only made reasonable guesses, in particular to obtain reasonable values of yearly inflation. All the numbers quoted below are not intended to be taken literally (although we believe they should be taken seriously!). II. A SHORT RECAP ON MARK-0 The Mark-0 model with a Central Bank (CB) and interest rates has been described in full details in [17, 19], where pseudo-codes are also provided. We will not repeat here the full logic of the model, but only focus on the elements that are relevant for determining inflation in the three sectors: households, firms and the CB. The pseudo-code of the model explored in this work is provided in Appendix B. First, we need some basic notions. The model is defined in discrete time, where the unit time between tand t+1 is plausibly of the order of months. For definiteness, we will choose in the following the unit time scale to be 6 months. Each firm iat time tproduces a quantity Yi(t) of perishable goods that it attempts to sell at price pi(t), and pays a wage Wi(t) to its employees. The demand Di(t) for good idepends on the global consumption budget of households CB(t), itself determined as an inflation rate-dependent fraction of the household savings. Diis a decreasing function of the firm price pi, with a price sensitivity parameter that can be tuned. To update their production, price and wage policy, firms use reasonable “rules of thumb” [17] that also depend on the inflation rate through their level of debt (see below). For example, production is decreased and employees are made redundant whenever Yi> Di, and vice-versa.2 The model is fully “stock-flow consistent” (i.e. all the stocks and flows within the toy economy are properly accounted for). The instantaneous inflation rate π(t) is defined as: π(t) = p(t)−p(t−1) p(t−1) ;p(t) = Pipi(t)Yi(t) PiYi(t),(1) where p(t) is the production-weighted average price. We will assume that firms, households and the CB do not react to the instantaneous value of π(t), but rather to a smoothed, exponential moving average πema(t), computed as πema(t) := ωπ(t) + (1 −ω)πema(t−1),(2) where we fix ω= 0.2, which corresponds to an averaging time of ≈4.5 time steps, i.e. roughly 2 years in our setting. In Mark-0 we assume a linear production function with a constant unit productivity, which means that output and employment coincide. The unemployment rate uis defined as: u(t) := 1 −PiYi(t) N,(3) where Nis the number of firms, which also coincides with the total workforce [17]. A. The Central Bank policy In this work, we consider a single-mandate CB that attempts to steer the economy towards a target inflation level π?(in [19], we in fact considered a double-mandate CB also targeting a certain employment level ε?). The monetary policy3followed by the CB for fixing the base interest rate is described by a standard Taylor-rule of the form [6, 23]: ρ0(t) = ρ?+φπ[πema(t)−π?] (4) 2As a consequence of these adaptive adjustments, the economy is on average always ‘close’ to the global market clearing condition one would posit in a fully representative agent framework. However, small fluctuations persists in the limit of large system sizes giving rise to a rich phenomenology [17], including business cycles. 3Note that this is in our model the only action taken by the CB to achieve the target; in particular, no actions on the quantity of circulating money, such as quantitative easing or printing money can be taken by the CB. 4 where ρ?is the “natural” interest rate and φπ>0 quantifies the intensity of the policy4. We assume that the banking sector sets the interest rates on deposits and loans (ρd(t) and ρ`(t) respectively) uniformly for all lenders and borrowers5. The rate ρ`increases and ρddecreases when firm defaults increase, in such a way that the banking sector – which fully absorbs these defaults – makes zero profit at each time step (see [19] for more details). B. Households The effect of inflation on households is the standard trade-off between investment (at rate ρd) and consumption. We therefore assume that the total consumption budget of households CB(t) is given by: CB(t) = c(t)S(t) + W(t) + ρd(t)S(t)with c(t) = [[c01 + αc(bπ(t)−ρd,ema(t))]]1 0,(5) where S(t) is the savings, W(t) the total wages, bπ(t) is the expected inflation in the next period – see Eq. (6) below – and c(t) is the consumption propensity, which is clipped to the interval [0,1]. This is expressed by the symbol [[x]]1 0 which means that the quantity xis boxed between 0 and 1, i.e. [[x]]1 0= 1 if x > 1, [[x]]1 0= 0 if x < 0, and [[x]]1 0=x otherwise. This propensity is equal to c0when the difference between expected inflation and the interest paid on their savings is zero, and increases (decreases) when this difference is positive (negative). The parameter αc>0 determines the sensitivity of households to the real interest rate. In spirit, Eq. (5) is similar to the standard Euler equation of DSGE models (see e.g. [6, 23]). We furthermore posit that the expected inflation bπ(t) is given by a linear combination of the realised inflation πema(t) and the CB target inflation π?(see also [21]): bπ(t) = τema πema(t) + τ?π?.(6) The parameters τema and τ?can be interpreted as capturing the trust of economic agents in the ability of the CB to enforce its inflation target. They are therefore expected to depend on the commitment of the CB, measured by the Taylor-rule parameter φpi. When τema = 0 and τ?= 1, agents fully trust that the target inflation will be realised. When τema >0, they are also influenced by the past realised inflation when they form their expectations. When τema >1, they expect more inflation to be realised in the next period. As we will see below, this can give rise to hyper-inflation episodes, which is the scenario that prevents (in the mind of many policy makers and of the public opinion) higher inflation targets. In principle, τema and τ?could themselves be time dependent, as economic agents compare the realised inflation to the target inflation and “learn” about the credibility of the CB – see below and [21] for a discussion of this point. In the present paper, we will treat τema and τ?as time independent. C. Firms 1. Financial fragility Each firm is characterized by its production Yi(equal to its workforce), demand for its goods Di, price pi, wage Wi and its cash balance Eiwhich, when negative, is the debt of the firm. We characterize the financial fragility of the firm through the debt-to-payroll ratio Φi=−Ei WiYi .(7) If Φi(t)<Θ, i.e. when the flux of credit needed from the bank is not too high compared to the size of the company (measured as the total payroll), the firm is allowed to continue its activity. If on the other hand Φi(t)≥Θ, the firm defaults and the corresponding default cost is absorbed by the banking sector. The parameter Θ controls the maximum leverage in the economy, and models the risk-control policy of the banking sector. 4Note that in our previous paper [19], we had φπ→10φπin Eq. (4). The factor 10, that was useful in the context of [19], has been eliminated here to conform with the standard definition. 5This is, in our model, the only role played by the banking sector: a transmission belt of the CB policy. In reality, the banking sector has much more freedom, and can sometimes make the CB policy ineffective, e.g. by restricting credit even in presence of a strong incentive from the CB. 5 2. Production update If the firm is allowed to continue its business, it adapts its price, wages and production according to reasonable “rules of thumb” – see [17, 19]. In particular, the production update is chosen as: If Yi(t)< Di(t)⇒Yi(t+ 1) = Yi(t) + min{η+ i(Di(t)−Yi(t)), u? i(t)} If Yi(t)> Di(t)⇒Yi(t+ 1) = Yi(t)−η− i[Yi(t)−Di(t)] (8) where u? i(t) is the maximum number of unemployed workers available to the firm iat time t(see [19, Appendix A]). The coefficients η±∈[0,1] express the sensitivity of the firm’s target production to excess demand/supply. We postulate that the production adjustment depends on the financial fragility Φiof the firm: firms that are close to bankruptcy are arguably faster to fire and slower to hire, and vice-versa for healthy firms. In order to model this tendency, we posit that the coefficients η± ifor firm i(belonging to [0,1]) are given by: η− i= [[η− 0(1 + ΓΦi(t))]]1 0 η+ i= [[η+ 0(1 −ΓΦi(t))]]1 0,(9) where η± 0are fixed coefficients, identical for all firms6. The factor Γ >0 measures how the financial fragility of firms influences their hiring/firing policy, since a larger value of Φithen leads to a faster downward adjustment of the workforce when the firm is over-producing, and a slower (more cautious) upward adjustment when the firm is under-producing. In [19] we argue that Γ should in fact depend on the difference between the interest rate and the inflation: high cost of credit makes firms particularly wary of going into debt and their sensitivity to their financial fragility is increased. Therefore, we postulate that interest rates influence the firm’s policy through the financial fragility sensitivity Γ, as: Γ = max {αΓ(ρ`,ema(t)−bπ(t)),0},(10) where αΓ(similarly to αcabove) captures the influence of the real interest rate on loans on the hiring/firing policy of the firms. 3. Price update Prices are updated through a random multiplicative process which takes into account the production-demand gap experienced in the previous time step and if the price offered is competitive (with respect to the average price). The update rule for prices reads: If Yi(t)< Di(t)⇒(If pi(t)<p(t)⇒pi(t+ 1) = pi(t)(1 + γξi(t))(1 + bπ(t)) If pi(t)≥p(t)⇒pi(t+ 1) = pi(t)(1 + bπ(t)) If Yi(t)> Di(t)⇒(If pi(t)> p(t)⇒pi(t+ 1) = pi(t)(1 −γξi(t))(1 + bπ(t)) If pi(t)≤p(t)⇒pi(t+ 1) = pi(t)(1 + bπ(t)) (11) where ξi(t) are independent uniform U[0,1] random variables and γis a parameter setting the relative magnitude of the price adjustment, chosen to be 0.1 throughout this work. The (1 + bπ(t)) factor implies that firms also anticipate inflation when they set their prices. This is precisely the dreaded self-reflexive mechanism that may lead to hyperinflation when expected future inflation is dominated by past realised inflation (the parameter τema), rather than by the CB inflation target (the parameter τ?). 6Note that in our previous work, the clipping was such that η± i∈[0,2η± 0]. This modification is irrelevant. 6 4. Wage update The wage update rule follows (in spirit) the choices made for price and production. At each time step firm iupdates the wage paid to its employees as: WT i(t+ 1) = Wi(t)[1 + γ(1 −ΓΦi)(1 −u(t))ξ0 i(t)](1 + gbπ(t)) if (Yi(t)< Di(t) Pi(t)>0 Wi(t+ 1) = Wi(t)[1 −γ(1 + ΓΦi)u(t)ξ0 i(t)](1 + gbπ(t)) if (Yi(t)> Di(t) Pi(t)<0 (12) where Pi(t) is the profit of the firm at time tand ξ0 i(t) an independent U[0,1] random variable. If WT i(t+ 1) is such that the profit of firm iat time twith this amount of wages would have been negative, Wi(t+ 1) is chosen to be exactly at the equilibrium point where Pi(t) = 0; otherwise Wi(t+ 1) = WT i(t+ 1). Finally, gis a certain parameter modulating the way wages are indexed to inflation. We will assume in the following full indexation (g= 1), but choosing g < 1 can be useful to stabilize the Mark-0 economy in periods of hyper-inflation. The above rules are intuitive: if a firm makes a profit and it has a large demand for its good, it will increase the pay of its workers. The pay rise is expected to be large if the firm is financially healthy and/or if unemployment is low because pressure on salaries is high. Conversely, if the firm makes a loss and has a low demand for its good, it will attempt to reduce the wages. This reduction is drastic is the company is close to bankruptcy, and/or if unemployment is high, because pressure on salaries is then low. In all other cases, wages are not updated. In essence, deeply indebted firms seek to reduce wages more rapidly, whereas flourishing firms tend to increase wages more quickly. Note that within the model the productivity of workers is not related to their wages. The only channel through which wages impact production is that the quantity u? i(t) that appears in Eq. (8), which represents the share of unemployed workers accessible to firm i, is an increasing function of Wi. Hence, firms that want to produce more (hence hire more) do so by increasing Wi, as to attract more applicants (see [19, Appendix A] for details). III. THE “NATIVE” STATE OF THE ECONOMY In [17, 19], we have shown that the Mark-0 economy, once set in motion, can settle in a variety of stationary macrostates, where the aggregate variables behave very differently. In our opinion, the strength of Agent Based modelling is precisely to show that micro-rules do matter, as they can lead to very different macro-states. We will not repeat such an analysis in full here, but focus on the role of a few variables, relevant to the topic of this paper. We start by analyzing the case where the CB does not react to inflation (i.e. the Taylor-rule Eq. (4) is with φπ= 0). We will see below how a Taylor-rule based policy of the Central Bank allows it to steer the economy towards a target level of inflation. Fig. 1 shows the phase diagram of the model in the plane (ρ?, R), where ρ?is the baseline interest rate and R=η+ 0/η− 0is the ratio of the hiring propensity to the firing propensity, that was shown to play a crucial role for determining the level of unemployment [17]. Unless explicitly stated, we fix throughout the paper γ= 0.1, c0= 0.5, η− 0= 0.2, Θ = 3, g= 1, αΓ= 50, αc= 4 (the last two parameters are as in [19]). Note that in the absence of an active CB, we posit that the implicit target inflation is such that π?≡ρ?and that τ?>0 even when φπ= 0. The color code in Fig. 1 gives the average unemployment hui(left plot) and inflation rate hπi(right plot). For a fixed value of R, we observe that for small values of ρ?, the economy is in a HIHO state (high inflation and high output/low unemployment), while for ρ?> ρ†(R) the economy tips over to a LILO state (low inflation and low output/high unemployment). The transition is driven by a drop both in household consumption and firm investments, induced by the high yield on savings and high cost of loans. As noted in the Introduction, the HIHO/LILO transition occurs discontinuously while the change of interest rate is continuous. The transition point ρ†(R) is, as expected, an increasing function of R(the economy is more stable where the hiring rate is larger than the firing rate); it is also a decreasing function of αΓsince firms refrain from taking loans to invest and continue their business when αΓis large [19]. Remarkably, the “native” state of the economy can display endogenous oscillations (or business cycles), as already noted in [17]. In the present case, such spontaneous oscillations occur in a small region around (ρ?= 4.5%, R = 0.75), see [17] for details. It is interesting to investigate the role of inflation expectations in this framework, by varying the value of τema. Fig. 2 shows the phase diagram of the model in the plane (ρ?, τema) for a fixed value of R= 0.8. As anticipated, a transition to a hyper-inflation, low output state (HYLO) occurs when expectations amplify inflation, more precisely 7 0.0 0.5 1.0 1.5 012345 ρ* R 25 50 75 100 <u> HIHO LILO 0.0 0.5 1.0 1.5 012345 ρ* R −5 0 5 10 <π> HIHO LILO FIG. 1: Average unemployment (left) and inflation (right) in the (ρ?, R) plane. The HIHO phase in the top region of the graph is separated from the LILO phase in the bottom region by a critical line ρ†(R). Other parameters are: τema =τ?= 0.5 and φπ= 0. Both inflation and natural rate are expressed as %/year, unemployment is expressed in % of the workforce. when τema > τ†≈1.1.7The full phase diagram is however quite complex, with a region of hyper-inflation but full employment (HYHO) when τema ≈1 and low enough values of ρ?. For larger values of ρ?(say, ρ?= 3% represented by the dotted line in Fig. 2) one observes a sequence of transitions as τema increases from zero: LILO →HIHO → HYHO →LILO →HYLO.8This illustrates the highly non-trivial role of inflation expectations in our framework: all possible states of the economy can be reproduced within this simple framework, including a virtuous state of high output and relatively low inflation (LIHO), stagflation (HILO) or even deflation (HDLO). 0.0 0.5 1.0 1.5 012345 ρ* τema 0 25 50 75 100 <u> HIHO LILO HYLO HYHO HILO LIHO HDLO LILO 0.0 0.5 1.0 1.5 012345 ρ* τema −5 0 5 10 <π> LILO HIHO LILO HYLO HYHO HILO LIHO HDLO FIG. 2: Average unemployment (left) and inflation (right) in the (ρ?, τema) plane. In the right panel, the grey area corresponds to the hyper-inflation region where inflation is not stationary, but constantly growing. The region τema &1.1 is a HYLO state (hyper-inflation, low output), but one can also end up in a HYHO state (hyper-inflation, high output) in a tongue-like grey region of the right plot. All other possibilities are present as well: HIHO, LILO, LIHO (bottom left region) and HILO (stagflation, see the “island” around the point ρ?= 1, τema = 1) or even deflation. Other parameters are: R= 0.8, τ?= 0.5 and φπ= 0. Both inflation and natural rate are expressed as %/year, unemployment is expressed in % of the workforce. IV. INFLATION TARGETING We now pick two representative states of the economy, one with ρ?= 1%/year corresponding to the the HIHO state, and the other with ρ?= 3%/year corresponding to the LILO state. The inflation level of these native states is, 7In the hyper-inflation phase, inflation itself grows with time, so the average inflation is undefined. 8There is even a thin sliver of hyper-deflation in Fig. 2. We have checked that this is not a numerical artefact 8 respectively, 4.7% and 0% while the unemployment rate is, respectively, 0.8% and 85%. The long run real return on savings hρd−πiis, respectively, −3.7% and 0%. The HIHO state discourages long term savings while the LILO state is vastly inefficient in terms of output. The CB steps in and modulates the interest rate according to the Taylor-rule, Eq. (4), with a standard value of φπ= 2.5 (i.e. an increase of inflation by 1% leads to the CB increasing the nominal base-line rate by 2.5%).9We assume that firms and agents form their inflation expectations by giving an equal weight to the target inflation π? and the realised inflation πema; in other words we set τema =τ?=1 2. We will also report the results when agents fully trust the CB policy (τema = 0, τ?= 1). In the other extreme case (τema = 1, τ?= 0), the CB policy is, as expected, totally inefficient (results not shown). The resulting states of the monitored economy are summarized in Figs. 3 and 4, where we show, as a function of the inflation target: the average unemployment hui, the average realised inflation hπi, the probability Pneg that the CB must impose negative rates and finally the average real interest rate paid on deposits hρd−πi. A. HIHO Starting from a HIHO native state, one sees that targeting a low inflation rate has a destabilizing effect and unemployment rockets to 95%, while realised inflation is below target (see Fig. 3 panel a). For our particular “fromthe-hip” choice of parameters, realised inflation reaches target when π?≈2% and overshoots beyond that point, but this allows unemployment, and the probability of negative rates, to be significantly reduced. For example, Pneg. plummets from ≈0.9 for π?= 1.25% to zero for π?>2%. Note that the real interest rate on deposits goes from significantly negative (−3.7%) in the native HIHO state to roughly zero when π?is in the range 2% – 2.5% in the monitored economy, while it remains negative outside that interval. Beyond π?= 2.5%, output continues to improve, but the real interest rates on savings dips. When π?= 3.25%, unemployment is however still around 20% and only falls below 5% when the target inflation exceeds 4%. The situation improves slightly when agents fully trust the ability of the CB to reach its target (i.e. τ?= 1 and τema = 0). Unemployment then falls below 5% as soon as π?>3%. In other words, stronger anchoring of inflation expectations is beneficial in our ABM setting, in agreement with the intuition gained from DSGE models. At variance with DSGE models, however, increased Taylor coefficients do lead to instabilities in our model (see [19]). Our setting highlights the difference between two policy transmission channels: behavioral biases, i.e. expectations based on historical data (τema), and rational anticipations resulting from a Taylor-rule-based intervention of the CB (φπ). So overall, increasing the inflation target closer to that of the native state is favorable, at least up to a point beyond which realised inflation significantly overshoots the target and interest rates on savings become strongly negative. Note that a similar pattern also applies to the virtuous low inflation/high outpout (LIHO) state: with a natural state of the economy having an inflation of ≈2.5%/year, targeting a too low inflation (below ≈2%/year) induces a strong growth of unemployment, with a similar qualitative pattern as in Fig. 3. B. LILO Let us now assume that the underlying economic mechanisms (described by the parameters of Mark-0) are such that the native state of the economy is LILO, for example when Ris small (firms are more reluctant to hire than to fire) or when ρ?or αΓare large (firms are more reluctant to take loans). In this case, the role of the CB is to kick start the economy by lowering the interest rate. The results of a Taylor-rule based policy are now shown in Fig. 4 as a function of the inflation target π?. Surprisingly, the dependence of huion π?is non-monotonic. As long as π? is below 3%, unemployment is in fact an increasing function of the inflation target, with very frequent periods of negative nominal rates. Unemployment reaches acceptable values only when π?is large enough. For example, when τ?= 0.5 and π?= 4%, unemployment is around 13% (down from 85% in the native state), long term real savings rate are close to zero and the probability of negative nominal rates is zero. 9Other values of φπhave been studied as well, with similar conclusions. Larger φπlead to higher unemployment and more frequent negative nominal rates, while smaller φπlead to more abrupt (and hence less manageable) dependencies of huiand hπion π?. It would be interesting to extend the present study to dual-mandate CBs. 15 Algorithm 2 Mark0 (continued) u←1−1 NFPiY[i].Update uand p p←Pip[i]Y[i] PiY[i] .Private bank sets interest rates ρ`=ρ0+ (1 −f)D/E− ρd=ρ`E−−D S+E+ .Households decide the demand S←(1 + ρd)S+PiW[i]Y[i] c←c0[1 + αc(bπ−eρd,ema)] CB←cS for (i←0; i < NF;i←i+ 1) do D[i]←CBa[i] exp(−βp[i]/p) p[i]Pia[i] exp(−βp[i]/p).Inactive firms have no demand end for .Accounting E+←0 for (i←0; i < NF;i←i+ 1) do if a[i] == 1 then S←S−p[i] min{Y[i], D[i]} P[i]←p[i] min{Y[i], D[i]} − W[i]Y[i] + ρdmax {E[i],0}+ρ`min {E[i],0} E[i]← E[i] + P[i] if P[i]>0 && E[i]>0then .Pay dividends S←S+δE[i] E[i]← E[i]−δE[i] end if E+← E++ max {E[i],0} end if end for .Revivals R ← 0 for (i←0; i < NF;i←i+ 1) do if a[i] == 0 then if random < ϕ then Y[i]←urandom a[i]←1 P[i]←p W[i]←w E[i]←W[i]Y[i] R ← R +E[i] E+← E++ max {E[i],0} end if end if end for for (i←0; i < NF;i←i+ 1) do if a[i] == 1 then if E[i]>0then E[i]← E[i]− RE[i]/E+ end if end if end for end for 16 [1] O. 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